1. Field of the Invention
The present invention relates to a method of generating reticle data, a memory medium storing a program for generating reticle data, and a method of producing a reticle.
2. Description of the Related Art
A semiconductor device is manufactured by repeating a photolithography process. The photolithography process includes an exposure process of exposing a substrate by illuminating a reticle (also called a mask or original) bearing a circuit pattern with exposure light, and projecting the circuit pattern onto a substrate (e.g., a wafer) via a projection optical system. Recent miniaturization of semiconductor devices requires formation of patterns with dimensions smaller than the wavelength of exposure light. However, the formation of such fine patterns is greatly affected by diffraction of light. The contour of a reticle pattern may not be directly formed on a substrate. The pattern may be rounded at the corner or shorten, or the shape accuracy may greatly decrease. To suppress such degradation, the shape of a reticle pattern is corrected. This correction is called optical proximity correction (OPC).
In conventional OPC, the shape of a reticle pattern is corrected by a rule base or a model base using optical simulation, by taking account of the shape of each figure of the reticle pattern and the influence of surrounding patterns.
In the model base OPC, a reticle pattern is repetitively deformed until a target pattern is obtained. As the method of deformation, various methods have been proposed. An example is a method (so-called iterative improvement) of, if critical dimension (CD) of the optical image is partially excessive, narrowing a reticle pattern by the same amount as the excess, and if CD of the optical image is partially insufficient, expanding the reticle pattern by the same amount. While the optical image is recalculated for the changed reticle pattern, a formed pattern is gradually deformed to match with a target pattern. A method using a genetic algorithm has also been proposed. A method of inserting an auxiliary pattern of a size small enough not to resolve is popular, too.
Japanese Patent Laid-Open Nos. 2004-221594 and 2005-183981 disclose methods of determining how to insert an auxiliary pattern by numerical calculation. According to this technique, an interference map is obtained by numerical calculation. A portion where patterns interfere constructively with each other on a reticle and a portion where they interfere destructively with each other are derived from the interference map. At a portion where patterns interfere constructively with each other on the interference map, an auxiliary pattern is inserted to make exposure light having passed through the aperture of a main pattern in phase with exposure light having passed through an auxiliary pattern. At a portion where patterns interfere destructively with each other on the interference map, an auxiliary pattern is inserted to make exposure light having passed through the aperture of a contact hole pattern serving as a main pattern 180° out of phase with exposure light having passed through an auxiliary pattern. Consequently, the main and auxiliary patterns interfere constructively with each other, forming a pattern almost equal to a target pattern on a substrate. The reticle surface and substrate surface have an imaging relationship, so that the interference map can be regarded as an electric field amplitude on the image plane.
Japanese Patent Laid-Open No. 2008-40470 also discloses a method of numerically obtaining information of an auxiliary pattern. A mask pattern and wafer pattern in a semiconductor exposure apparatus have a partial coherent imaging relationship. In the partial coherent imaging, an aerial image can be calculated by obtaining the coherence on the mask surface from information of an effective light source and performing Fourier integration based on the coherence and the spectral distribution (diffracted light distribution) of a mask. The “coherence” herein mentioned is the degree of interference corresponding to the distance on the mask surface. The “effective light source” is a light intensity distribution formed on the pupil of a projection optical system without any mask.
The coherence of the effective light source can be considered using a transmission cross coefficient (TCC). The TCC is defined on the pupil plane of a projection optical system, and is the portion where the effective light source, the pupil function of the projection optical system, and the complex conjugate of the pupil function of the projection optical system overlap.
According to the method disclosed in Japanese Patent Laid-Open No. 2008-40470, the TCC function is two-dimensionally expressed by fixing the pupil position, thereby obtaining an aerial image. Based on the aerial image, an auxiliary pattern is placed near a peak position expect for a pattern to be resolved.
According to the method disclosed in Japanese Patent Laid-Open No. 2005-183981, for example, a contact hole pattern is replaced with a Dirac delta function. The delta function and a point spread function are convoluted to generate an interference map. An auxiliary pattern with a transmittance of 100% and a phase shift of 0° is placed in a region in which the interference map takes a positive value. An auxiliary pattern with a transmittance of 100% and a phase shift of 180° is placed in a region in which the interference map takes a negative value.
According to the method disclosed in Japanese Patent Laid-Open No. 2008-40470, a contact hole is regarded as a pattern with a nonzero size, and an aerial image is calculated by a TCC function. Then, an auxiliary pattern with a transmittance of 100% and a phase shift of 0° is placed in a region in which the aerial image takes a positive value. An auxiliary pattern with a transmittance of 100% and a phase shift of 180° is placed in a region in which the aerial image takes a negative value.
However, neither reference considers the possibility that an auxiliary pattern with a phase shift of 0° and that with a phase shift of 180° partially overlap each other, and processing executed upon overlapping.